The Nature of Computation

Erscheinungsjahr 2013
ISBN: 978-0-19-923321-2
Verlag: ACADEMIC

Buch, Englisch, 1008 Seiten, Print PDF, Format (B × H): 194 mm x 252 mm, Gewicht: 2099 g

Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. But this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results like interactive proofs, phase transitions, and quantum computing are usually considered too advanced for the typical student. This book bridges these gaps by explaining the deep ideas of theoretical computer science in a clear and enjoyable fashion, making them accessible to non-computer scientists and to computer scientists who finally want to appreciate their field from a new point of view. The authors start with a lucid and playful explanation of the P vs. NP problem, explaining why it is so fundamental, and so hard to resolve. They then lead the reader through the complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing. At every turn, they use a minimum of formalism, providing explanations that are both deep and accessible. The book is intended for graduate and undergraduate students, scientists from other areas who have long wanted to understand this subject, and experts who want to fall in love with this field all over again.

Zielgruppe

First-year graduate students in computer science; instructors in theoretical computer science; graduate students in mathematics, physics, engineering, and theoretical biology. Statistical and quantum physicists interested in the interdisciplinary boundary between physics and computer science; scientists from mathematics, physics, engineering, and theoretical biology who are interested in computational complexity; motivated undergraduates in computer science and the above fields.

Autoren/Hrsg.

Moore, Cristopher

Mertens, Stephan

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik EDV | Informatik Informatik Berechenbarkeitstheorie, Komplexitätstheorie
• Mathematik | Informatik EDV | Informatik Informatik Theoretische Informatik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

- 1: Prologue

- 2: The Basics

- 3: Insights and Algorithms

- 4: Needles in a Haystack: The class NP

- 5: Who is the Hardest One of All: NP-Completeness

- 6: The Deep Question: P vs. NP

- 7: Memory, Paths and games

- 8: Grand Unified Theory of Computation

- 9: Simply the Best: Optimization

- 10: The Power of Randomness

- 11: Random Walks and Rapid Mixing

- 12: Counting, Sampling, and Statistical Physics

- 13: When Formulas Freeze: Phase Transitions in Computation

- 14: Quantum Computing

- 15: Epilogue

- 16: Appendix: Mathematical Tools

Über Autor(innen)

Moore, Cristopher
Cristopher Moore, Computer Science Department and Department of Physics and Astronomy, University of New Mexico, and External Professor, Santa Fe Institute

Mertens, Stephan
Stephan Mertens, Institute of Theoretical Physics, Otto-von-Guericke University, Magdeburg, and External Professor, Santa Fe Institute

Cristopher Moore graduated from Northwestern University with honors in 1986, at the age of 18, with a B.A. in Mathematics, Physics, and Integrated Science. He received his Ph.D. in Physics from Cornell University at the age of 23. After a postdoc at the Santa Fe Institute, he joined the faculty of the University of New Mexico, where he holds joint appointments in Computer Science and Physics and Astronomy. He has written over 90 papers, on topics ranging from undecidability in dynamical systems, to quantum computing, to phase transitions in NP-complete problems, to the analysis of social and biological networks.

Stephan Mertens got his Diploma in Physics in 1989, and his Ph.D. in Physics in 1991, both from Georg-August University Göttingen. He holds scholarships from the "Studienstiftung des Deutschen Volkes", Germany's most prestigious organisation sponsoring the academically gifted. After his Ph.D. he worked for three years in the software industry before he joined the faculty of Otto-von-Guericke University Magdeburg as a theoretical physicist. His research focuses on disordered systems in statistical mechanics, average case complexity of algorithms, and parallel computing.